Question

Solve the following equations, and check for extraneous solutionsa)(x-8)/(x-4)=2b)(4x-8)/(x-2)=4

Answer 1

Answer:

a) x = 0 is the solution to the equation.

b) x = any real number except 2

Step-by-step explanation:

Hi there!

a) First, let´s write the equation:

(x-8) / (x-4) = 2

Now let´s solve it for x. Let´s start subtracting 2 to both sides of the equation

[(x-8) / (x-4)]  - 2 = 0

Let´s subtract both terms, the least common multiple is (x-4)

[x-8 - 2(x - 4)] / (x-4) = 0

Apply distributive property

(x - 8 - 2x + 8) / (x - 4) = 0

-x / (x-4) = 0

x = 0

Now, let´s check the solution:

(x-8) / (x-4) = 2

x = 0

0-8 / 0-4 = 2

-8/-4 = 2

2 = 2

Then x = 0 is the solution to the equation.

b) Let´s write the equation:

(4x-8)/(x-2)=4

Let´s proceed in the same way as in a)

Subtract 4 to both sides of the equation.

(4x-8)/(x-2) - 4 = 0

Subtract both terms

[4x - 8 - 4(x-2)] / (x-2) = 0

Apply distributive property

(4x -8 - 4x + 8) / (x -2) = 0

0/(x-2) = 0

x can be any real number except 2 because it would make the denominator zero.